Suppose a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. Hint: Write an equation using two points in the form (x,p). A company’s revenue is the amount of money that comes in from sales, before business costs are subtracted. For a single product, you can find the revenue by multiplying the quantity of the product sold, x, by the demand equation, p. Substitute the result you found from part a. into the equation R = xp to find the revenue equation. Provide your answer in simplified form.

(42,20),(52,10) are two points.

THe standard two point form is p-p1=m(x-x1).

m-(y2-y1)/(x2-x1)=(10-20)/(52-42)=-1.

p-20=-1(x-42).

p=-x+42+20

=-x+62

p=-x+62 is the required equation in the form p=mx+b.

R=xp=x(-x+62)=-x^2+62x.

Revinue equation R=-x^2+62x.